S. Duquesne, Improving the arithmetic of elliptic curves in the Jacobi model, Information Processing Letters, vol.104, issue.3, pp.101-105, 2007.
DOI : 10.1016/j.ipl.2007.05.012

URL : https://hal.archives-ouvertes.fr/lirmm-00145805

P. Gaudry, Fast genus 2 arithmetic based on Theta functions, Journal of Mathematical Cryptology, vol.1, issue.3, pp.243-265, 2007.
DOI : 10.1515/JMC.2007.012

URL : https://hal.archives-ouvertes.fr/inria-00000625

P. Gaudry and . Schost, On the Invariants of the Quotients of the Jacobian of a Curve of Genus 2, Lecture Notes in Comput. Sci, vol.2227, pp.373-386, 2001.
DOI : 10.1007/3-540-45624-4_39

URL : https://hal.archives-ouvertes.fr/inria-00514434

A. Kruppa, Factoring into large primes with P-1, P+1 and ECM, 2008.

H. W. Lenstra and J. , Factoring Integers with Elliptic Curves, The Annals of Mathematics, vol.126, issue.3, pp.126-649, 1987.
DOI : 10.2307/1971363

P. L. Montgomery, Evaluating recurrences of form x m+n = f (xm, xn, x m?n ) via Lucas chains Available at ftp.cwi.nl/pub/pmontgom/Lucas.ps.gz. 8. , Speeding the Pollard and Elliptic Curve Methods of Factorization, Math. Comp, issue.177, pp.48-243, 1983.

D. Mumford, Tata lectures on theta I, Tata lectures on theta II, 1983.
DOI : 10.1007/978-1-4899-2843-6

T. Shaska, Genus two curves covering elliptic curves: a computational approach, Computational Aspects of Algebraic Curves, pp.151-195, 2005.
DOI : 10.1142/9789812701640_0013

P. Van-wamelen, Equations for the Jacobian of a hyperelliptic curve, Transactions of the American Mathematical Society, vol.350, issue.08, pp.3083-3106, 1998.
DOI : 10.1090/S0002-9947-98-02056-X

L. and C. Scientifique, 54506 Vandoeuvre-l` es-Nancy , France E-mail address: romain.cosset@loria